It's useful information, and it doesn't even show up in the game log. Only way to tell is to watch the fast animation of where the card goes after it's played. It currently says "Mander is cursed, and then passes the curse along." Requesting change to "Mander is cursed, and then passes the curse along to [whoever]".
A good idea indeed. Though there's another way you can keep track of that without paying attention to the animation: Keep track of the number of cards on your deck. If you play the travelling curse, take a quick look before and after at the enemy deck count. If your enemy played travelling curse, add up the amount of cards on hand, discard and deck for each of your char (ignore any racial move card). As long as no Battlefield training is used, a number > 30 is the person who got the travelling curse.
That doesn't work in campaign, because enemy decks aren't a standard size. Also, that only works in MP if there's only one curse traveling around. Presumably if one were building some sort of traveling curse party, there'd be many curses which would travel.
I'd like this change. I greatly enjoy seeing who's going to suffer the Traveling Curse next. (And hopefully see it's someone who didn't build a deck to accommodate it. You know.)
Is travelling curse so popular that people actually meta against it??! There goes my awesome curse deck...